Bring the milk, butter, salt, and cayenne to a boil in a saucepan. Remove from the heat, add the flour all at once, and mix vigorously with a wooden spatula until the mixture forms a ball. Return the pan to the heat and cook over medium heat, stirring occasionally, for about 1 minute to dry the mixture a bit. Transfer to the bowl of a food processor, let cool for 5 minutes, then process for about 5 seconds.

Add the eggs and paprika to the processor bowl, and process for 10 to 15 seconds, until well mixed. Transfer the choux paste to a mixing bowl, and let cool for 10 minutes.

Preheat the oven to 375°. Line a cookie sheet with a reusable nonstick baking mat or parchment paper. Reserve 1 tablespoon of the grated Parmesan cheese, then add the remainder and all the Swiss cheese to the choux paste. Stir just enough to incorporate. Using a tablespoon, scoop out a level tablespoon of the gougère dough, and push it off the spoon onto the cooking mat. Continue making individual gougères, spacing them about 2-inches apart on the sheet. Sprinkle a few grains of coarse salt and a little of the reserved Parmesan cheese on each gougère. Bake for about 30 minutes, until nicely browned and crisp. Serve lukewarm or at room temperature with drinks.